If \(U=\mathbb R\), \(A=\{x:-1\le x<5\}\), and \(B=\{x:2<x\le 8\}\), what is \(A'\cup B'\)?
Advertisement
Answer and explanation
Correct answer: \((- infty,2]\cup[5,\infty)\)
By De Morgan’s law, \(A'\cup B'=(A\cap B)'\). The common part of \(A=[-1,5)\) and \(B=(2,8]\) is \((2,5)\); both endpoints are excluded because 2 is not in \(B\) and 5 is not in \(A\). The real-number complement of \((2,5)\) is \((- infty,2]\cup[5,\infty)\).
Frequently asked questions
What is the correct answer to this question?
\((- infty,2]\cup[5,\infty)\)
Why is this the correct answer?
By De Morgan’s law, \(A'\cup B'=(A\cap B)'\). The common part of \(A=[-1,5)\) and \(B=(2,8]\) is \((2,5)\); both endpoints are excluded because 2 is not in \(B\) and 5 is not in \(A\). The real-number complement of \((2,5)\) is \((- infty,2]\cup[5,\infty)\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
Advertisement